We are given a triangle where the perimeter is $11x + 7$, and two sides of the triangle are labeled as $5x + 5$ and $3x - 1$. We need to find the missing side length, which I will call $y$.

The formula for the perimeter of a triangle is the sum of all three sides. Therefore:

$\text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Side}_3$

Substitute the known values:

$11x + 7 = (5x + 5) + (3x - 1) + y$

Now, let's solve for $y$.

First, simplify the equation:

$11x + 7 = 5x + 5 + 3x - 1 + y$

Combine like terms on the right-hand side:

$11x + 7 = 8x + 4 + y$

Now, isolate $y$:

$y = 11x + 7 - 8x - 4$

Simplify further:

$y = 3x + 3$

So, the missing side length is $y = 3x + 3$.

Would you like further details or have any additional questions?

Here are five related questions to consider:

1. What happens to the side lengths when specific values of $x$ are substituted?
2. How would the solution change if the perimeter were altered?
3. Can this triangle be classified as a specific type (like equilateral or isosceles) based on the side lengths?
4. How would you calculate the area of this triangle given specific side lengths?
5. What is the relationship between the perimeter and area of a triangle?

Tip: Always double-check if an expression simplifies easily, as it can speed up problem-solving.